# Find in implicit form, the general solution of a differential equation

• Mar 7th 2013, 12:11 PM
landmark
Find in implicit form, the general solution of a differential equation
I was asked to show that ∫ (1+e^4x)/〖(4x+e^4x)〗^3 dx= -1/(8(4x+e^3x )^2 )+c (x>0)
And I did.
But the next question goes "hence find, in implicit form, the general solution of the differential equation dy/dx= -(〖4e〗^(-2y) (1+e^4x ))/(4x+e^4x )^3 (x>0)"

I am not sure what to do can I get some help please
• Mar 7th 2013, 01:03 PM
HallsofIvy
Re: Find in implicit form, the general solution of a differential equation
Well, the obvious thing to do is to convert the differential equation to an integral isn't it?
$\displaystyle \frac{dy}{dx}= \frac{4e^{2y}(1+ e^{4x})}{(4x+ e^{4x})^3}$
so $\displaystyle \frac{dy}{ye^{2y}}= \frac{(1+ e^{4x})}{(4x+ e^{4x})^3}dx$
• Mar 7th 2013, 01:09 PM
landmark
Re: Find in implicit form, the general solution of a differential equation
I have tried that but seem to end up in a bit of a mess
• Mar 7th 2013, 01:11 PM
landmark
Re: Find in implicit form, the general solution of a differential equation
Actually I think I have it now, Thanks